Question: Simplify; express your answer in exponential form. Assume $y\neq 0, k\neq 0$. $\dfrac{{(y^{2})^{-2}}}{{(y^{3}k)^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{2}}$ to the exponent ${-2}$ . Now ${2 \times -2 = -4}$ , so ${(y^{2})^{-2} = y^{-4}}$ In the denominator, we can use the distributive property of exponents. ${(y^{3}k)^{2} = (y^{3})^{2}(k)^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{2})^{-2}}}{{(y^{3}k)^{2}}} = \dfrac{{y^{-4}}}{{y^{6}k^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-4}}}{{y^{6}k^{2}}} = \dfrac{{y^{-4}}}{{y^{6}}} \cdot \dfrac{{1}}{{k^{2}}} = y^{{-4} - {6}} \cdot k^{- {2}} = y^{-10}k^{-2}$.